ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_distUnifPar::setUnifParRand Interface Reference

Return a random vector from the \(\ndim\)-dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.
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Detailed Description

Return a random vector from the \(\ndim\)-dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.

See the documentation of pm_distUnifPar for details of the definition of the PDF.

Parameters
[in,out]rand: The input/output vector of shape (1:ndim) of,
  1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).
On input, it must contain a vector of randomly uniformly-distributed numbers in the range \([0, 1)\).
On output, it will contain a random vector from the support of the target distribution.
[in]lb: The input scalar or contiguous vector of the same type and kind as the output argument rand.
  1. If ub is a scalar, then lb must be a scalar representing the lower bound of the ndim-dimensional hyper-cube support of the distribution.
  2. If ub is a vector, then lb must be a vector representing the lower bound of the ndim-dimensional hyper-rectangle support of the distribution.
  3. If ub is a matrix, then lb must be a vector representing the origin of the coordinate system with respect to which the ndim-dimensional hyper-parallelepiped support of the distribution is determined.
(optional. default = 0)
[in]ub: The input scalar or contiguous vector/matrix of the same type and kind as the output argument rand.
  1. If ub is a scalar, it must contain the upper bound of the ndim-dimensional hyper-cube support of the distribution.
    In such a case, the input optional argument ndim must be specified.
  2. If ub is a vector of shape (1:ndim), it must contain the upper bounds of the ndim-dimensional hyper-rectangle support of the distribution along each dimension.
  3. If ub is a square matrix of shape (1:ndim, 1:ndim), it must contain the representative matrix of the ndim-dimensional hyper-parallelepiped support of the distribution.


Possible calling interfaces

call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), ub) ! Uniform Hyper-cube support starting at the origin.
call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), lb, ub) ! Uniform Hyper-cube support with lower bound `lb`.
call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), ub(1:ndim)) ! Uniform Hyper-rectangle support starting at the origin.
call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), lb(1:ndim), ub(1:ndim)) ! Uniform Hyper-rectangle support with lower bound `lb`.
call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), ub(1:ndim, 1:ndim)) ! Uniform Hyper-parallelepiped support starting at the origin.
call random_number(rand(1:ndim))
call setUnifParRand(rand(1:ndim), lb(1:ndim), ub(1:ndim, 1:ndim)) ! Uniform Hyper-parallelepiped support starting at `lb`.
!
Return a random vector from the -dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.
This module contains classes and procedures for setting up and computing the properties of the MultiV...
Warning
The condition all(0. <= rand .and. rand < 1.) must hold for the corresponding input arguments.
The condition all(size(rand) == size(lb(:))) must hold for the corresponding input arguments.
The condition all(size(rand) == shape(ub)) must hold for the corresponding input arguments.
The condition all(lb /= ub(:)) must hold for the corresponding input arguments.
Although there is theoretically no limit on the possible values of lb and ub with respect to each other, the condition all(lb(:) < ub(:)) is expected (but not checked) to hold for the corresponding input arguments.
The input representative matrix of the parallelepiped support of the distribution ub(:,:) must be non-singular.
In other words, the columns of the matrix must span the \(\mathbb{R}^{\ndim}\) space.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_io, only: display_type
6
7 implicit none
8
9 real :: rand(5)
10
11 type(display_type) :: disp
12 disp = display_type(file = "main.out.F90")
13
14 call disp%skip()
15 call disp%show("call random_number(rand(1:2))")
16 call random_number(rand(1:2))
17 call disp%show("call setUnifParRand(rand(1:2), ub = 1.)")
18 call setUnifParRand(rand(1:2), ub = 1.)
19 call disp%show("rand(1:2)")
20 call disp%show( rand(1:2) )
21 call disp%skip()
22
23 call disp%skip()
24 call disp%show("call random_number(rand(1:2))")
25 call random_number(rand(1:2))
26 call disp%show("call setUnifParRand(rand(1:2), lb = -100., ub = 1.)")
27 call setUnifParRand(rand(1:2), lb = -100., ub = 1.)
28 call disp%show("rand(1:2)")
29 call disp%show( rand(1:2) )
30 call disp%skip()
31
32 call disp%skip()
33 call disp%show("call random_number(rand(1:5))")
34 call random_number(rand(1:5))
35 call disp%show("call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.")
36 call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.])
37 call disp%show("rand(1:5)")
38 call disp%show( rand(1:5) )
39 call disp%skip()
40
41 call disp%skip()
42 call disp%show("call random_number(rand(1:5))")
43 call random_number(rand(1:5))
44 call disp%show("call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.")
45 call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.])
46 call disp%show("rand(1:5)")
47 call disp%show( rand(1:5) )
48 call disp%skip()
49
50 call disp%skip()
51 call disp%show("call random_number(rand(1:2))")
52 call random_number(rand(1:2))
53 call disp%show("call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))")
54 call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))
55 call disp%show("rand(1:2)")
56 call disp%show( rand(1:2) )
57 call disp%skip()
58
59 call disp%skip()
60 call disp%show("call random_number(rand(1:2))")
61 call random_number(rand(1:2))
62 call disp%show("call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))")
63 call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))
64 call disp%show("rand(1:2)")
65 call disp%show( rand(1:2) )
66 call disp%skip()
67
68 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
69 ! Output an example array for visualization.
70 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
71
72 block
73 use pm_arraySpace, only: setLinSpace
74 real :: rand(2, 4)
75 integer(IK) :: fileUnit, i
76 open(newunit = fileUnit, file = "setUnifParRand.RK.txt")
77 do i = 1, 1000
78 call random_number(rand)
79 call setUnifParRand(rand(:,1), lb = -[2., 2.], ub = -[0., 1.])
80 call setUnifParRand(rand(:,2), ub = reshape([1., 1., -1., +1.], shape = [2, 2]))
81 call setUnifParRand(rand(:,3), lb = [2.0, -2.], ub = reshape([1., 1., +2., -2.], shape = [2, 2]))
82 call setUnifParRand(rand(:,4), lb = [1.5, -.5], ub = reshape([2., 1., 1., 2.], shape = [2, 2]))
83 write(fileUnit, "(*(g0,:,','))") rand
84 end do
85 close(fileUnit)
86 end block
87
88end program example
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output
1
2call random_number(rand(1:2))
3call setUnifParRand(rand(1:2), ub = 1.)
4rand(1:2)
5+0.446436286, +0.106434882
6
7
8call random_number(rand(1:2))
9call setUnifParRand(rand(1:2), lb = -100., ub = 1.)
10rand(1:2)
11-86.5660019, -58.6573372
12
13
14call random_number(rand(1:5))
15call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.
16rand(1:5)
17+0.441022336, +0.249059796, +1.95939755, +3.76885104, +1.25133538
18
19
20call random_number(rand(1:5))
21call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.
22rand(1:5)
23-0.207175374, -0.693487883, +0.384066582, -1.06522036, +2.45016193
24
25
26call random_number(rand(1:2))
27call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))
28rand(1:2)
29-0.752362728, -0.752362728
30
31
32call random_number(rand(1:2))
33call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))
34rand(1:2)
35+9.10447311, +9.10447311
36
37

Postprocessing of the example output
1#!/usr/bin/env python
2
3import matplotlib.pyplot as plt
4import pandas as pd
5import numpy as np
6import glob
7import sys
8
9linewidth = 2
10fontsize = 17
11
12for kind in ["RK"]:
13
14 pattern = "*." + kind + ".txt"
15 fileList = glob.glob(pattern)
16
17 for file in fileList:
18
19 df = pd.read_csv(file, delimiter = ",", header = None)
20
21 # definitions for the axes
22 #left, width = 0.1, 0.65
23 #bottom, height = 0.1, 0.65
24 #spacing = 0.015
25
26 # start with a square Figure
27 fig = plt.figure(figsize = (8, 6))
28
29 plt.rcParams.update({'font.size': fontsize - 2})
30 ax = plt.subplot()
31 #ax = fig.add_axes([left, bottom, width, height]) # scatter plot
32 #ax_histx = fig.add_axes([left, bottom + height + spacing, width, 0.2], sharex = ax) # histx
33 #ax_histy = fig.add_axes([left + width + spacing, bottom, 0.2, height], sharey = ax) # histy
34 #
35 #for axes in [ax, ax_histx, ax_histy]:
36 # axes.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
37 # axes.tick_params(axis = "y", which = "minor")
38 # axes.tick_params(axis = "x", which = "minor")
39 #
40
43
44 # the scatter plot:
45 for i in range(0, len(df.values[0,:]), 2):
46 ax.scatter ( df.values[:,i]
47 , df.values[:,i+1]
48 , s = 8
49 , zorder = 1000
50 )
51
52 #ax_histx.hist(df.values[:, 0], bins = 50, zorder = 1000)
53 #ax_histy.hist(df.values[:, 1], bins = 50, orientation = "horizontal", zorder = 1000)
54
55 ax.set_aspect("equal")
56 ax.set_xlabel("X", fontsize = 17)
57 ax.set_ylabel("Y", fontsize = 17)
58 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
59 plt.minorticks_on()
60
61 plt.tight_layout()
62 plt.savefig(file.replace(".txt",".png"))

Visualization of the example output
Test:
test_pm_distUnifPar


Final Remarks


If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

  1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
  2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Author:
Amir Shahmoradi, April 23, 2017, 12:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 920 of file pm_distUnifPar.F90.


The documentation for this interface was generated from the following file: